A Serrin-type over-determined problem for Hessian equations in the exterior domain

Bo Wang; Zhizhang Wang

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arXiv · 2412.11841

A Serrin-type over-determined problem for Hessian equations in the exterior domain

Bo Wang·Zhizhang Wang

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Abstract

In this paper, we consider the Hessian equations in some exterior domain with prescribed asymptotic behavior at infinity and Dirichlet-Neumann conditions on its interior boundary. We obtain that there exists a unique bounded domain such that the over-determined problem admits a unique strictly convex solution.

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Bo Wang, Zhizhang Wang. 2024-12-16. A Serrin-type over-determined problem for Hessian equations in the exterior domain. https://arxiv.org/abs/2412.11841

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